Wei Jianming, Zhang Youan, Sun Meimei, Geng Baoliang
Department of Control Engineering, Naval Aeronautical and Astronautical University, Yantai 264001, PR China.
Department of Electrical and Electronic Engineering, Yantai Nanshan University, Yantai 265713, PR China.
ISA Trans. 2017 Sep;70:79-92. doi: 10.1016/j.isatra.2017.05.007. Epub 2017 May 23.
This paper presents an adaptive iterative learning control scheme for a class of nonlinear systems with unknown time-varying delays and control direction preceded by unknown nonlinear backlash-like hysteresis. Boundary layer function is introduced to construct an auxiliary error variable, which relaxes the identical initial condition assumption of iterative learning control. For the controller design, integral Lyapunov function candidate is used, which avoids the possible singularity problem by introducing hyperbolic tangent funciton. After compensating for uncertainties with time-varying delays by combining appropriate Lyapunov-Krasovskii function with Young's inequality, an adaptive iterative learning control scheme is designed through neural approximation technique and Nussbaum function method. On the basis of the hyperbolic tangent function's characteristics, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.
本文针对一类具有未知时变延迟且控制方向之前存在未知非线性类反冲滞后的非线性系统，提出了一种自适应迭代学习控制方案。引入边界层函数来构造辅助误差变量，这放宽了迭代学习控制的相同初始条件假设。对于控制器设计，使用积分李雅普诺夫函数候选，通过引入双曲正切函数避免了可能的奇异性问题。通过将适当的李雅普诺夫 - 克拉索夫斯基函数与杨氏不等式相结合来补偿时变延迟的不确定性后，通过神经逼近技术和努斯鲍姆函数方法设计了一种自适应迭代学习控制方案。基于双曲正切函数的特性，通过在两种情况下构造类李雅普诺夫复合能量函数（CEF），证明系统输出收敛到期望轨迹的一个小邻域，同时保持所有闭环信号有界。最后，给出一个仿真例子来验证所提方法的有效性。
